Can I vent New bathroom vent into dryer vent line?

I want to add a ceiling vent to the bathroom. We currently have a washer/dryer setup in the same room just divided by articulating doors. The window that the the dryer vents thru is glass block and to try to avoid tearing that up, is there some way I can tie a bathroom fan vent line into the dryer vent line? I was looking for some type of a check valve or something that would keep the dryer exhaust from going to the fan and untimately into the room. I had figured on using a y instead of a t to help the exhaust head toward the window instead of the new ceiling fan. The next closest window is about 20 feet away and on the other side of a wall plus this is a basement bathroom so the kitchen is directly above so there is not an option to vent up thru the roof as a direct line.

That is what my common sense tells me as well, but I wanted to make sure there was not a 'check valve' of sorts that would allow me to do that. The dryer is electric, but I understand and had thought of the backflow that is why I just wanted to make sure an item did not exist. The only reason for trying to do it is that the glass block window is in line with a wall. One glass block on the left of the wall that is actually a flap vent for the dryer and the other 3 glass blocks on the right of the wall are actually one half block then a double block wide hopper window then another half block wide glass block. Right now we open the window to let moisture out but I wanted to add a fan for conveience sake.

I ran across the power vents for dryers so I didn't know if there was such a thing to combine the two vents already in existance but known as a last resort fix.

Which way do the floor joists run? If from where you want to put the fan to the outside wall, then it shouldn't be too bad to run the vent through the ceiling to the outside. If they run the other way, it might still be possible, but it would have to go much further.